Leading Order Hadronic Contribution Research Articles

The detector for the MUonE experiment at CERN

The detector for the MUonE experiment at CERN

An alternative evaluation of the leading-order hadronic contribution to the muon g − 2 with MUonE

An alternative evaluation of the leading-order hadronic contribution to the muon g − 2 with MUonE

Measurement of e+e− → π+π−π0 at BABAR and calculation of (g−2)μ

Measurement of e+e− → π+π−π0 at BABAR and calculation of (g−2)μ

Single π0 production in μe scattering at MUonE

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision prediction in radiative corrections to the $\mu e$ scattering as well as for robust quantitative estimates of all possible background processes. In this letter, the contribution due to the emission of a neutral pion through the process $\mu e \to \mu e \pi^0$ is studied and its numerical impact is discussed in different phase space configurations by means of the upgraded Monte Carlo event generator MESMER. In fact, single $\pi^0$ production could be a source of reducible background for the measurement of the QED running coupling constant at MUonE and it could be also an important background for possible New Physics searches at MUonE involving $2 \to 3$ processes, in phase space regions complementary to the ones characteristic of the elastic $\mu e$ scattering.

Study of the process e+e−→π+π−π0 using initial state radiation with BABAR

The process e+e−→π+π−π0γ is studied at a center-of-mass energy near the ϒ(4S) resonance using a data sample of 469 fb−1 collected with the BABAR detector at the PEP-II collider. We have performed a precise measurement of the e+e−→π+π−π0 cross section in the center-of-mass energy range from 0.62 to 3.5 GeV. In the energy regions of the ω and ϕ resonances, the cross section is measured with a systematic uncertainty of 1.3%. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured e+e−→π+π−π0 cross section from threshold to 2.0 GeV is (45.86±0.14±0.58)×10−10. From the fit to the measured 3π mass spectrum we have determined the resonance parameters Γ(ω→e+e−)B(ω→π+π−π0)=(0.5698±0.0031±0.0082) keV, Γ(ϕ→e+e−)B(ϕ→π+π−π0)=(0.1841±0.0021±0.0080) keV, and B(ρ→3π)=(0.88±0.23±0.30)×10−4. The significance of the ρ→3π signal is greater than 6σ. For the J/ψ resonance we have measured the product Γ(J/ψ→e+e−)B(J/ψ→3π)=(0.1248±0.0019±0.0026) keV.21 MoreReceived 4 October 2021Accepted 12 November 2021DOI:https://doi.org/10.1103/PhysRevD.104.112003Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle interactionsPhysical SystemsLight mesonsQuarkoniaTechniquesLepton collidersParticle productionParticles & Fields

NNLO virtual and real leptonic corrections to muon-electron scattering

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The fixed-order NNLO radiative corrections due to the emission of virtual and real leptonic pairs are described and their numerical impact is discussed for typical event selections of the MUonE experiment, by means of the upgraded Monte Carlo code Mesmer.

Towards muon-electron scattering at NNLO

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The theoretical formulation for the fixed-order NNLO photonic radiative corrections is described and the impact of the numerical results obtained with the corresponding Monte Carlo code is discussed for typical event selections of the MUonE experiment. In particular, the gauge-invariant subsets of corrections due to electron radiation as well as to muon radiation are treated exactly. The two-loop contribution due to diagrams where at least two virtual photons connect the electron and muon lines is approximated taking inspiration from the classical Yennie-Frautschi-Suura approach. The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be ultimately needed for data analysis.

Muon-electron scattering at NLO

We consider the process of muon-electron elastic scattering, which has been proposed as an ideal framework to measure the running of the electromagnetic coupling constant at space-like momenta and determine the leading-order hadronic contribution to the muon g−2 (MUonE experiment). We compute the next-to-leading (NLO) contributions due to QED and purely weak corrections and implement them into a fully differential Monte Carlo event generator, which is available for first experimental studies. We show representative phenomenological results of interest for the MUonE experiment and examine in detail the impact of the various sources of radiative corrections under different selection criteria, in order to study the dependence of the NLO contributions on the applied cuts. The study represents the first step towards the realisation of a high-precision Monte Carlo code necessary for data analysis.

Precision measurement of the hadronic contribution to the muon anomalous magnetic moment

We report on a precision measurement of the cross section for the reaction $e^+e^-\to\pi^+\pi^-$ in the mass range $0.30<M_{\pi\pi}<1.00$ GeV with the initial state radiation (ISR) method, using 817 pb$^{-1}$ of data at $e^+e^-$ center-of-mass energies near 3.77 GeV and 586 pb$^{-1}$ of data at $e^+e^-$ center-of-mass energies near 4.17 GeV, collected with the CLEO-c detector at the CESR $e^+e^-$ collider at Cornell University. The integrated cross sections in the range $0.30<M_{\pi\pi}<1.00$ GeV for the process $e^+e^-\to\pi^+\pi^-$ are determined with a statistical uncertainty of $0.7\%$ and a systematic uncertainty of $1.5\%$. The leading-order hadronic contribution to the muon anomalous magnetic moment calculated using these measured $e^+e^-\to\pi^+\pi^-$ cross sections in the range $M_{\pi\pi}=0.30$ to 1.00 GeV is calculated to be $(500.4\pm3.6 (\mathrm{stat})\pm 7.5(\mathrm{syst}))\times10^{-10}$.

Chiral extrapolation of the leading hadronic contribution to the muon anomalous magnetic moment

A lattice computation of the leading-order hadronic contribution to the muon anomalous magnetic moment can potentially help reduce the error on the Standard Model prediction for this quantity, if sufficient control of all systematic errors affecting such a computation can be achieved. One of these systematic errors is that associated with the extrapolation to the physical pion mass from values on the lattice larger than the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 200 to 400MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various tricks to improve the reliability of the chiral extrapolation employed in the literature are taken into account. In addition, while chiral perturbation theory also predicts the dependence on the pion mass of the leading-order hadronic contribution to the muon anomalous magnetic moment as the chiral limit is approached, this prediction turns out to be of no practical use, because the physical pion mass is larger than the muon mass that sets the scale for the onset of this behavior.

Measuring the leading hadronic contribution to the muon g-2 via mu e scattering

We propose a new experiment to measure the running of the electromagnetic coupling constant in the space-like region by scattering high-energy muons on atomic electrons of a low-Z target through the elastic process mu , e rightarrow mu , e. The differential cross section of this process, measured as a function of the squared momentum transfer t=q^2<0, provides direct sensitivity to the leading-order hadronic contribution to the muon anomaly a^mathrm{{HLO}}_{mu }. By using a muon beam of 150 GeV, with an average rate of sim 1.3 times 10^7 muon/s, currently available at the CERN North Area, a statistical uncertainty of sim 0.3% can be achieved on a^mathrm{{HLO}}_{mu } after two years of data taking. The direct measurement of a^mathrm{{HLO}}_{mu } via mu e scattering will provide an independent determination, competitive with the time-like dispersive approach, and consolidate the theoretical prediction for the muon g-2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon g-2 experiments at Fermilab and J-PARC.

Measuring the leading-order hadronic contribution to the muon g-2 in the space-like region

A new experiment is proposed to measure the running of the electromagnetic coupling constant in the space-like region by scattering high-energy muons on atomic electrons of a low-Z target. The differential cross section of the elastic process μe → μe provides direct sensitivity to the leading-order hadronic contribution to the muon anomaly aμ HLO . It is argued that by using the 150-GeV muon beam available at the CERN North Area, with an average rate of ~ 1.3 × 107 muon/s, a statistical uncertainty of ~ 0.3% can be achieved on aμ HLO after two years of data taking. The direct measurement of aμ HLO via μe scattering will provide an independent determination and consolidate the theoretical prediction for the muon g -2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon g -2 experiments at Fermilab and JPARC.

Theoretical determination of the hadronic g − 2 of the muon

An approach is discussed on the determination of the leading order hadronic contribution to the muon anomaly, [Formula: see text], based entirely on theory. This method makes no use of [Formula: see text] annihilation data, a likely source of the current discrepancy between theory and experiment beyond the 3[Formula: see text] level. What this method requires is essentially knowledge of the first derivative of the vector current correlator at zero-momentum. In the heavy-quark sector, this is obtained from the well-known heavy-quark expansion in perturbative quantum chromodynamics (QCD), leading to values of [Formula: see text] in the charm- and bottom-quark region which were fully confirmed by later lattice QCD (LQCD) results. In the light-quark sector, using recent preliminary LQCD results for the first derivative of the vector current correlator at zero-momentum leads to the value [Formula: see text], which is significantly larger than values obtained from using [Formula: see text] data. A separate approach based on the operator product expansion (OPE), and designed to quench the contribution of these data, reduces the discrepancy by at least 40%. In addition, it exposes a tension between the OPE and [Formula: see text] data, thus suggesting the blame for the discrepancy on the latter.

A Hybrid Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to (g − 2)μ

Abstract The leading-order hadronic contribution to the muon anomalous magentic moment, a μ LO,HVP , can be expressed as an integral over Euclidean Q 2 of the vacuum polarization function. We point out that a simple trapezoid-rule numerical integration of the current lattice data is good enough to produce a result with a less-than-1% error for the contribution from the interval above Q 2 ≳ 0.1 − 0.2 GeV 2 . This leaves the interval below this value of Q 2 as the one to focus on in the future. In order to achieve an accurate result also in this lower window Q 2 ≲ 0.1 − 0.2 GeV 2 , we indicate the usefulness of three possible tools. These are: Pade Approximants, polynomials in a conformal variable and a NNLO Chiral Perturbation Theory representation supplemented by a Q 4 term. The combination of the numerical integration in the upper Q 2 interval together with the use of these tools in the lower Q 2 interval provides a hybrid strategy which looks promising as a means of reaching the desired goal on the lattice of a sub-percent precision in the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

Finite-volume effects in the muon anomalous magnetic moment on the lattice

We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. We consider both recent lattice data as well as lowest-order, finite-volume chiral perturbation theory, in order to get a quantitative understanding. Even though leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a good representation of finite-volume effects. We find that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the leading-order hadronic contribution to the muon anomalous magnetic moment, even when using ensembles with $m_\pi L> 4$ and $m_\pi \sim 200$ MeV.

Leading-order hadronic contributions to the lepton anomalous magnetic moments from the lattice

The hadronic leading-order (hlo) contribution to the lepton anomalous magnetic moments $a_l^\mathrm{hlo}$ of the Standard Model leptons still accounts for the dominant source of the uncertainty of the Standard Model estimates. We present the results of an investigation of the hadronic leading order anomalous magnetic moments of the electron, muon and tau lepton from first principles in twisted mass lattice QCD. With lattice data for multiple pion masses in the range $230 \mathrm{~MeV} \lesssim m_{PS} \lesssim 490 \mathrm{~MeV}$, multiple lattice volumes and three lattice spacings we perform the extrapolation to the continuum and to the physical pion mass and check for all systematic uncertainties in the lattice calculation. As a result we calculate $a_{l}^\mathrm{hlo}$ for the three Standard Model leptons with controlled statistical and systematic error in agreement with phenomenological determinations using dispersion relations and experimental data. In addition, we also give a first estimate of the hadronic leading order anomalous magnetic moments from simulations directly at the physical value of the pion mass.

Leading-order hadronic contribution to the electron and muong− 2

I present a new data driven update of the hadronic vacuum polarization effects for the muon and the electron $g-2$. For the leading order contributions I find $a_\mu^{\mathrm{had}(1)}=(686.99\pm 4.21)[687.19\pm 3.48]\times 10^{-10}$ based on $e^+e^-$data [incl. $\tau$ data], $a_\mu^{\mathrm{had}(2)}= (-9.934\pm 0.091) \times 10^{-10}$ (NLO) and $a_\mu^{\mathrm{had}(3)}= (1.226\pm 0.012) \times 10^{-10}$ (NNLO) for the muon, and $a_e^{\mathrm{had}(1)}=(184.64\pm 1.21)\times 10^{-14}$ (LO), $a_e^{\mathrm{had}(2)}=(-22.10\pm 0.14)\times 10^{-14}$ (NLO) and $a_e^{\mathrm{had}(3)}=(2.79\pm 0.02)\times 10^{-14}$ (NNLO) for the electron. A problem with vacuum polarization undressing of cross-sections (time-like region) is addressed. I also add a comment on properly including axial mesons in the hadronic light-by-light scattering contribution. My estimate here reads $a_\mu[a_1,f_1',f_1] \sim ({ 7.51 \pm 2.71}) \times 10^{-11}\,.$ With these updates $a_\mu^{\rm exp}-a_\mu^{\rm the}=(32.73\pm 8.15)\times 10^{-10}$ a 4.0 $\sigma$ deviation, while $a_e^{\rm exp}-a_e^{\rm the}=(-1.10\pm 0.82)\times 10^{-12}$ shows no significant deviation.

Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD

The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weak mixing angle, $\theta_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.

New strategy for the lattice evaluation of the leading order hadronic contribution to(g−2)μ

A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid-rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval $Q^2>Q^2_{min}$, coupled with an $N$-parameter Pad\'e or other representation of the polarization in the interval $0<Q^2<Q^2_{min}$, for sufficiently high $Q^2_{min}$ and sufficiently large $N$. Using a physically motivated model for the $I=1$ polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of $Q^2_{min}$ and $N$ can be reduced to well below the 1% level for $Q^2_{min}$ as low as 0.1 GeV$^2$ and rather small $N$. For such low $Q^2_{min}$, both an NNLO chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-$Q^2$ contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a sub-percent precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

Status of Leading-Order Hadronic Vacuum Polarization Dispersion Calculation

The leading-order hadronic contribution to the muon magnetic anomaly a_{\mu} = (g_{\mu} - 2)/2, calculated using a dispersion integral of e+e- annihilation data and tau decay data, is briefly reviewed. This contribution has the largest uncertainty to the predicted value of a_{\mu}, which differs from the experimental value by ~3.6 (2.4) standard deviations for the e+e- (tau) based analysis. New results since the last workshop and main open issues on the subject are discussed.